# Equation of all planes passing through the given line?

We are given a line $$\overrightarrow r = \lambda(\hat i-\hat j+\hat k)$$ which is the intersection of planes $$x+y=0$$ and $$y+z=0$$.

How do I find the equation all planes passing through $$\overrightarrow r$$ ?

$$\alpha(x+y)+\beta(y+z)=0$$, $$\alpha,\beta\in\mathbb{R}$$, $$\alpha^2+\beta^2\ne0$$
• Nevermind, got it. I think instead of $\alpha$ it will be just 1. Thanks. – Raghav May 1 at 16:10
• $\alpha(x+y)+\beta(y+z)=0$ incldues all planes passing through $\vec{r}$ except $y+z=0$. – CY Aries May 1 at 16:14